14 ms·

The classic text on analysis is Principles of Mathematical Analysis by Rudin. Its very difficult and leaves it to the reader to understand the terse proofs. It

The classic text on analysis is Principles of Mathematical Analysis by Rudin. Its very difficult and leaves it to the reader to understand the terse proofs. It starts from the beignning, with no math background assumed about the reader. The terse proofs are written in such a way to force the reader to gain deep mathematical intuition. Some of the proofs are elegant and beautiful. I would absolutely recommend it. You can see a pdf here: https://notendur.hi.is/vae11/%C3%9Eekking/principles_of_mathematical_analysis_walter_rudin.pdf https://notendur.hi.is/vae11/%C3%9Eekking/principles_of_math...

bordercases 6y ago
> It starts from the beignning, with no math background assumed about the reader. It assumes that you have enough mathematical maturity to deal with proofs left to the reader.
- chynaman 6y ago
  IMO, Rudin is difficult not because of its proofs or lack of them (many proofs in discrete math can be no less brutal than anything in Rudin), rather that it's almost completely and utterly devoid of illuminating examples. For example, the definitions of "neighborhood", "limit point", "closed set", "open set", "bounded set", "perfect set", dense set" are crammed into a single definition 2.18 in chapter 2(Topology in Euclidean Spaces) in 3rd edition. The rest of the chapter is made up of theorems and corollaries. No related examples. On the other hand, Raffi Grinberg's analysis book meant to guide one through Rudin's book spends a whole chapter on elaborating on 2.18. And to be honest even that is barely adequate (totally inadequate, actually) if one wishes to become technically proficient in dealing with basic concepts in analysis with ease (that requires exposure to lots and lots of different examples). Although, probably, neither book has the latter as their goal.

14 ms·

The classic text on analysis is Principles of Mathematical Analysis by Rudin. Its very difficult and leaves it to the reader to understand the terse proofs. It

by logicslave 6y ago

bordercases 6y ago
> It starts from the beignning, with no math background assumed about the reader. It assumes that you have enough mathematical maturity to deal with proofs left to the reader.
- chynaman 6y ago
  IMO, Rudin is difficult not because of its proofs or lack of them (many proofs in discrete math can be no less brutal than anything in Rudin), rather that it's almost completely and utterly devoid of illuminating examples. For example, the definitions of "neighborhood", "limit point", "closed set", "open set", "bounded set", "perfect set", dense set" are crammed into a single definition 2.18 in chapter 2(Topology in Euclidean Spaces) in 3rd edition. The rest of the chapter is made up of theorems and corollaries. No related examples. On the other hand, Raffi Grinberg's analysis book meant to guide one through Rudin's book spends a whole chapter on elaborating on 2.18. And to be honest even that is barely adequate (totally inadequate, actually) if one wishes to become technically proficient in dealing with basic concepts in analysis with ease (that requires exposure to lots and lots of different examples). Although, probably, neither book has the latter as their goal.